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Abstract

We present the language PC+ for probabilistic reasoning about actions, which is a generalization of the action language C+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of PC+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.

Citations

...our framework further semantic notions like counterfactuals, interventions, actual cause, and causal explanations, taking inspiration by similar concepts in the structural-model approach to causality =-=[15, 9]-=-. Acknowledgments This work was partially supported by FWF (Austrian Science Funds) under the projects P14781-INF, P16536-N04, and Z29-N04 and by the European Commission under the grant FET-2001-37004...

...alternatives. We define a formal semantics of PC+ by interpreting probabilistic action descriptions in PC+ as probabilistic transitions as in partially observable Markov decision processes (POMDPs) [=-=11]-=-. However, it is important to point out that these probabilistic transitions are between sets of states rather than single states. It is this which allows to handle qualitative uncertainty in addition...

... for expressing qualitative uncertainty about the effects of actions and the initial situation of the world through disjunctive knowledge. Moreover, there are generalizations of the action language A =-=[6]-=- that allow for qualitative uncertainty in the form of nondeterministic actions. An important recent formalism in this family is the action language C+ [7], which is based on the theory of nonmonotoni...

...are generalizations of the action language A [6] that allow for qualitative uncertainty in the form of nondeterministic actions. An important recent formalism in this family is the action language C+ =-=[7-=-], which is based on the theory of nonmonotonic causal reasoning presented in [13], and has evolved from the action Alternate address: Institut fur Informationssysteme, Technische Universitat Wien, F...

...rtainty in the form of nondeterministic actions. An important recent formalism in this family is the action language C+ [7], which is based on the theory of nonmonotonic causal reasoning presented in =-=[13-=-], and has evolved from the action Alternate address: Institut fur Informationssysteme, Technische Universitat Wien, Favoritenstrae 9-11, A-1040 Vienna, Austria; e-mail: lukasiewicz@kr.tuwien.ac.at. ...

...n on the set of possible alternatives, and thus can numerically distinguish between possible alternatives. Well-known first-order formalisms for reasoning about actions such as the situation calculus =-=[18]-=- easily allow for expressing qualitative uncertainty about the effects of actions and the initial situation of the world through disjunctive knowledge. Moreover, there are generalizations of the actio...

...first-order logics of probability, and which allows to reason about an agent's probabilistic degrees of belief and how these beliefs change when actions are executed. Poole's independent choice logic =-=[16, 17] is based -=-on acyclic logic programs under different &quot;choices&quot;. Each choice along with the acyclic logic program produces a first-order model. By placing a probability distribution over the different c...

...our framework further semantic notions like counterfactuals, interventions, actual cause, and causal explanations, taking inspiration by similar concepts in the structural-model approach to causality =-=[15, 9]-=-. Acknowledgments This work was partially supported by FWF (Austrian Science Funds) under the projects P14781-INF, P16536-N04, and Z29-N04 and by the European Commission under the grant FET-2001-37004...

...ic effects of actions, C+ also supports concurrent actions as well as indirect effects and preconditions of actions through static causal laws. Closely related to it is the recent planning language K =-=[3]-=-. There are a number of formalisms for probabilistic reasoning about actions. In particular, Bacchus et al. [1] propose a probabilistic generalization of the situation calculus, which is based on firs...

...ions through static causal laws. Closely related to it is the recent planning language K [3]. There are a number of formalisms for probabilistic reasoning about actions. In particular, Bacchus et al. =-=[1]-=- propose a probabilistic generalization of the situation calculus, which is based on first-order logics of probability, and which allows to reason about an agent's probabilistic degrees of belief and ...

...obtain a distribution over the set of first-order models. Other probabilistic extensions of the situation calculus are given in [12, 5]. A probabilistic extension of the action language A is given in =-=[2]-=-. The main idea behind the present paper is to orthogonally combine qualitative and quantitative uncertainty in a uniform framework for reasoning about actions: Even though there is extensive work on ...

... placing a probability distribution over the different choices, we then obtain a distribution over the set of first-order models. Other probabilistic extensions of the situation calculus are given in =-=[12, 5]-=-. A probabilistic extension of the action language A is given in [2]. The main idea behind the present paper is to orthogonally combine qualitative and quantitative uncertainty in a uniform framework ...

...first-order logics of probability, and which allows to reason about an agent's probabilistic degrees of belief and how these beliefs change when actions are executed. Poole's independent choice logic =-=[16, 17] is based -=-on acyclic logic programs under different &quot;choices&quot;. Each choice along with the acyclic logic program produces a first-order model. By placing a probability distribution over the different c...

... placing a probability distribution over the different choices, we then obtain a distribution over the set of first-order models. Other probabilistic extensions of the situation calculus are given in =-=[12, 5]-=-. A probabilistic extension of the action language A is given in [2]. The main idea behind the present paper is to orthogonally combine qualitative and quantitative uncertainty in a uniform framework ...